The average monthly salary of all the employees of a firm is Rs. 60. Out of these employees, 12 officers receive an average salary of Rs. 400 per month and the rest receive an average of Rs. 56 per month. How many employees are there in the firm?

Introduction / Context:
This salary based question illustrates how a combined average arises from two subgroups with different averages. You know the overall average salary for all employees, the number and average salary of officers, and the average salary of the remaining employees. From this information, you must determine the total number of employees. This type of mixture and average problem is very common in quantitative aptitude tests.

Given Data / Assumptions:
- Let the total number of employees be N.
- Overall average salary of all employees = Rs. 60 per month.
- Number of officers = 12.
- Average salary of officers = Rs. 400 per month.
- Average salary of remaining employees = Rs. 56 per month.
- We need to find N.

Concept / Approach:
The overall average salary comes from the total salary paid to all employees divided by the total number of employees. The total salary can be expressed as the sum of the salary paid to officers plus the salary paid to the remaining employees. By writing this total in two different ways and equating them, we can solve for the total number of employees N.

Step-by-Step Solution:
Step 1: Total salary paid to all employees = overall average * total number of employees = 60 * N.Step 2: Salary paid to officers = number of officers * average officer salary = 12 * 400 = Rs. 4800.Step 3: Number of remaining employees = N - 12.Step 4: Total salary paid to remaining employees = (N - 12) * 56.Step 5: Total salary for all employees can also be written as 4800 + 56 * (N - 12).Step 6: Equate both expressions for total salary: 60 * N = 4800 + 56 * (N - 12).Step 7: Expand the right side: 60N = 4800 + 56N - 672.Step 8: Simplify: 60N = 56N + 4128, so 60N - 56N = 4128.Step 9: This gives 4N = 4128, so N = 4128 / 4 = 1032.

Verification / Alternative Check:
If N = 1032, then remaining employees = 1032 - 12 = 1020. Total salary for officers = 4800. Total salary for others = 1020 * 56 = 57120. Combined total salary = 4800 + 57120 = 61920. Dividing this by 1032 gives 61920 / 1032 = 60, which matches the given overall average salary. So N = 1032 is consistent.

Why Other Options Are Wrong:
Values like 1030, 1060 or 1062 do not satisfy the equation 60N = 4800 + 56(N - 12). Substituting any of these into the equation leads to a mismatch between the total salary based on the overall average and the sum of subgroup salaries.

Common Pitfalls:
Students sometimes forget to subtract 12 officers when computing the number of remaining employees, or they mistakenly average the salaries instead of working with totals. The safest path is always to convert every average into a total amount of salary and then form a simple linear equation in N.

Final Answer:
The firm has 1032 employees.